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A NOTE ON SIMPLE ZEROS OF PRIMITIVE DIRICHLET $L$-FUNCTIONS

Part of: Zeta and $L$-functions: analytic theory

Published online by Cambridge University Press:  08 July 2015

KEIJU SONO
KEIJU SONO*
Affiliation:
Tokyo Denki University, Muzaigakuendai, Inzai, Chiba, Japan email souno@mail.dendai.ac.jp
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Abstract

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In this paper, by using the theory of reproducing kernel Hilbert spaces and the pair correlation formula constructed by Chandee et al. [‘Simple zeros of primitive Dirichlet $L$-functions and the asymptotic large sieve’, Q. J. Math.65(1) (2014), 63–87], we prove that at least 93.22% of low-lying zeros of primitive Dirichlet $L$-functions are simple in a proper sense, under the assumption of the generalised Riemann hypothesis.

Keywords

primitive Dirichlet L-functionssimple zerospair correlation formulareproducing kernel

MSC classification

Primary: 11M26: Nonreal zeros of $zeta (s)$ and $L(s, chi)$; Riemann and other hypotheses
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 93 , Issue 1 , February 2016 , pp. 19 - 30
Copyright
© 2015 Australian Mathematical Publishing Association Inc. 

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